In the middle ages, peasant rebellions were dealt with by massacring the insurgents. The problem was that assembling a force to deal with a group could take a while, during which the poor had the run of the town. Smaller armed groups could also roam the countryside, and getting a force to hunt them down took long enough that they would be gone by the time it was assembled.

With an organized, professional force, you almost always have enough men on hand to deal with disturbances small and large. Part of the promise of a modern police force is that however well-armed you are, you can't win in the end: they'll always be able to call more reinforcement.

One funny thing is that you now have a bunch of idle police officers, who don't really have anything useful to do from day to day. So you use them to harass poor people, because, hey, why not?